Conflicts are faced by every organization, group of people, or even individuals in their daily life. If you think that only you feel the conflict of starting a particular job over others. Then you’ve got it wrong, there are many other people facing the same issue.
Often when you have a lot of tasks to establish in a day, you get confused. This confusion is usually about which task to accomplish first & how much time to devote to a particular task.
Do you know our system also faces a very common conflict? This conflict is named the painters partition problem. You must have heard the name of this problem while dealing with the flatten linked list situation.
Yes, this name is derived from a real-life problem.
It is based on the fact that a certain board can not be painted by two painters at a time. The issues faced by painters will be with the time taken by the painter to paint N number of boards.
Along with it, the issues might cover topics like space or area on the board, or preference. Similarly in the system, a board of memory units can not be partially covered by two different pieces of data.
Also, do you think that in a series of boards kept beside one another, a painter will paint only the odd or even numbered boards? No, the painters paint the continuous boards kept in a series.
Let’s have a detailed look at this problem and how the painters partition problem is resolved using codes.
What is the painters partition problem?
Painters partition problem is faced by the system when there is n number of boards on the system to be covered.
It can be understood with a simple protocol. The N number of boards are available on the system to be painted by the K number of painters. However, each painter belonging to the K array will take one unit of time at an instant to paint the board completely.
Now, all you need to do is to find out the minimum time taken by the K painters to paint N number of boards.
However, one constraint Or regulation is applied in this case. That is, the painters in K arrays will only paint the contagious boards. Also, at a given instant of time, it can not be done partially by another painter.
There are some constraints or rules that are applied to painters partition problems. They are:
- A single board must be painted by an individual painter. It will not be painted partially by one painter and another member of the painter array.
- Boards kept beside each other will be painted by the painters only. This means that the painter will not be allowed to paint 3rd board after 1st (skipping 2nd)
Now that you have understood how the constraints work in a painter partition problem, it’s time to discuss the approach to solve this problem.
The approach of painters partition problem
Searching for a minimum value of the lengths offered to each member of the array of painters to complete all the boards is the goal of this problem.
Therefore, you will have to adopt a specific approach to find the value of the minimum time taken by a set of painters to paint N number of boards by allotting the appropriate length of the board to any painter.
To find the value, you will have to run the array through a binary search. This binary search will yield appropriate results for you containing a range of answers that are possible and accurate to an extent.
Under ideal conditions the minimum time value is zero. However, the maximum value can go up to the sum of the overall product of the length of boards and the time taken to paint a unit.
Since the time parameter is constant and can be multiplied afterward, the main concern is to minimize the length provided to any of the painters to the maximum extent.
This means you have to minimize the length that can be allotted to a painter (utmost length)
Hence, to find the optimized value, you now have to run a binary search from the value zero-sum of the length of all the boards.
You will get a restriction or threshold value once you run your search. Store this value and check whether it is feasible to provide space to each painter without exceeding the limit i.e. crossing the threshold value.
You can shift to the right or left based on the status with the threshold value. This will help you to allot balanced value to the painters without surpassing the threshold value.
Once you follow this approach appropriately you will find the minimum value for the length that you can provide to the painters without any conflicts or issues.
After deciding on the approach for this problem you have to select a particular solution for it. For this, you need to know how and what values you will provide as input.
This code takes various values and data types as inputs that we have explained in the next segment to make it easier for you.
Input for painters partition problem
The code generated for this problem will take different data types in three stages. These stages are:
- In the first stage, an array or a value of A is inserted. This data type belongs to integer format and can be any integer.
- In the second argument, a different value says B will be offered to the code. This value will also be Inserted in a form of integer
- In the last and final argument, this code will take another value for C. The final argument will also be in an integer form.
Once you pass these arguments to the code, the appropriate output will be generated.
Inserting these arguments will provide you with an output with the format given in the next section.
The output of Painters partition problem
Since the values inserted in the code are integers, you will get the return in the same data type.
The output of this problem will provide you with a minimum time value that painters need to paint the boards. Given that they only paint the boards placed right after one another.
Only continuous sections of the board are painted by the painters during this minimum time that you have found as an output.
Bonus Topic – Linked Lists
If you don’t know much about the linked list and how to implement it in JavaScript, the below piece of information will help you.
A linked list is one of the most common types of data structures used by programmers. However, knowing this concept is not enough to resolve painters partition problems.
You must learn how to apply the concepts of linked lists, especially how to remove loop in linked list in various programming languages.
One of the highly demanded languages nowadays is JavaScript. Therefore, you should know how to implement the linked lists in JavaScript.
But, before implementing you should have the knowledge about the type of linked list. There are three main types of linked lists available in programming.
Types Of Linked List
As mentioned above, you will find three major types of linked lists in programming. Following are the types of linked lists:
- Single: In various linked lists, the data nodes have only one attachment i.e. pointer attached to it on either end of the node. In this, each node only has the pointer to the next node and the tail is missing. Since only one end is attached or pointed, this type is known as a singly linked list.
- Double: In a doubly linked list, each node has two attachments i.e. tail and pointer. In this type of linked list, each node is connected to the next node as well as the node placed previous to it in the lists.
- Circular: As the name suggests, in this type of linked list, each node pointer is directed from the tail of the other node. This generates a circular formation of nodes and hence, a linked list is called a circular linked list.
After determining the type of linked list you wish to implement, the next step is to implement them through functions. All the functions and operations are elaborated on in the upcoming section to make this process easier and more convenient for you.
Understanding the terms of a linked list and working on the implementation process is necessary to learn how to remove the loop in a linked list and provide an accurate solution to resolve the painter’s partition problem.
With the guidelines written above, now you will be able to implement a linked list without any error or hindrance. You will also be able to carry out similar coding problems with much ease..
Winding up
The partition problem is one of the most tricky problems faced by programmers right after you flatten a linked list.
However, with the right constraints and the accurate solution you can resolve this problem in no time.
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